Answer:
678-8
Explanation:
The given graph has a constant of proportionality equal to \dfrac{3}{4}
4
3
start fraction, 3, divided by, 4, end fraction.
This means that all yyy-values in this relationship are \dfrac{3}{4}
4
3
start fraction, 3, divided by, 4, end fraction of the xxx-value.
Which other relationships have the same constant of proportionality?
Hint #22 / 7
Let's pick a point from the given graph and get its \greenD{x}xstart color #1fab54, x, end color #1fab54- and \maroonD{y}ystart color #ca337c, y, end color #ca337c-values. We can use the point (\greenD{8},\maroonD{6})(8,6)left parenthesis, start color #1fab54, 8, end color #1fab54, comma, start color #ca337c, 6, end color #ca337c, right parenthesis.
Let's see whether that pair makes the equation 6\maroonD{y}=8\greenD{x}6y=8x6, start color #ca337c, y, end color #ca337c, equals, 8, start color #1fab54, x, end color #1fab54 true.
6\cdot \maroonD{6}\\eq8\cdot \greenD{8}6⋅6
=8⋅86, dot, start color #ca337c, 6, end color #ca337c, does not equal, 8, dot, start color #1fab54, 8, end color #1fab54
The equation does not have the same constant of proportionality.
Hint #33 / 7
Let's try the point (\greenD{8},\maroonD{6})(8,6)left parenthesis, start color #1fab54, 8, end color #1fab54, comma, start color #ca337c, 6, end color #ca337c, right parenthesis in the equation \maroonD{y}=\dfrac{3}{4}\greenD{x}y=
4
3
xstart color #ca337c, y, end color #ca337c, equals, start fraction, 3, divided by, 4, end fraction, start color #1fab54, x, end color #1fab54, too. Does that pair of values make the equation true?
\maroonD{6}\stackrel{\checkmark}{=}\dfrac{3}{4}\cdot \greenD{8}6
=
✓
4
3
⋅8start color #ca337c, 6, end color #ca337c, equals, start superscript, \checkmark, end superscript, start fraction, 3, divided by, 4, end fraction, dot, start color #1fab54, 8, end color #1fab54
The equation \maroonD{y}=\dfrac{3}{4}\greenD{x}y=
4
3
xstart color #ca337c, y, end color #ca337c, equals, start fraction, 3, divided by, 4, end fraction, start color #1fab54, x, end color #1fab54 has the same constant of proportionality as the graph.
Hint #44 / 7
Let's pick a point on the line to figure out the constant of proportionality. For the point (\greenD{2},\maroonD{1})(2,1)left parenthesis, start color #1fab54, 2, end color #1fab54, comma, start color #ca337c, 1, end color #ca337c, right parenthesis, the \maroonD{y}ystart color #ca337c, y, end color #ca337c-value is \dfrac12
2
1
start fraction, 1, divided by, 2, end fraction times the \greenD{x}xstart color #1fab54, x, end color #1fab54-value, not \dfrac34
4
3
start fraction, 3, divided by, 4, end fraction.
This relationship has a constant of proportionality of \dfrac12
2
1
start fraction, 1, divided by, 2, end fraction, not \dfrac34
4
3
start fraction, 3, divided by, 4, end fraction.
Hint #55 / 7
xxx yyy
333 444
121212 161616
151515 202020
In this table, all the \maroonD{y}ystart color #ca337c, y, end color #ca337c-values are \dfrac{4}{3}
3
4
start fraction, 4, divided by, 3, end fraction of the \greenD{x}xstart color #1fab54, x, end color #1fab54-values.
The constant of proportionality for this table is \dfrac{4}{3}
3
4
start fraction, 4, divided by, 3, end fraction instead of \dfrac{3}{4}
4
3
start fraction, 3, divided by, 4, end fraction.
Hint #66 / 7
xxx yyy
444 333
121212 999
141414 10.510.510, point, 5
In this table, every \maroonD{y}ystart color #ca337c, y, end color #ca337c-value is \dfrac{3}{4}
4
3
start fraction, 3, divided by, 4, end fraction of its corresponding \greenD{x}xstart color #1fab54, x, end color #1fab54-value.
The constant of proportionality for this table is \dfrac{3}{4}
4
3
start fraction, 3, divided by, 4, end fraction.
Hint #77 / 7
These are the relationships that have the same constant of proportionality between yyy and xxx as the given graph:
y=\dfrac{3}{4}xy=
4
3
xy, equals, start fraction, 3, divided by, 4, end fraction, x
xxx yyy
444 333
121212 999
141414 10.510.510, point, 5